## The 3-Sphere

So far we have seen geometries in 2D and 3D, which are the dimensions we are familiar with.  But mathematician have found interesting geometries in higher dimensions and it would be great if we could visualize them.  In particular a huge … Continue reading

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## Mandelbrot Set

If you google “mathematics visualization”, the resulting wikipedia page shows the Mandelbrot set as a famous example. The Mandelbrot set $$M\subset{\Bbb C}$$ is defined as the following.  For each $$c\in {\Bbb C}$$, consider the iteration $$z_{n+1}(c) = ({z_n}(c))^2+c$$, $$n=0,1,2,\ldots$$ and \(z_0(c) = … Continue reading

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## Parallel Frame for Curves

If you have a polygonal curve, say arc-length parameterized, you might want to visualize the curve as the following rendering This can be done in Houdini by the “copy” SOP node. The “copy” node has two input and one output.  The … Continue reading

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